The scene where Milo fights against the demons of Ignorance might be upsetting, especially when a bunch of demons form a mega-demon (that then dissolves after Milo throws a pencil at it). Tock also "dies" during this last battle, but then is revived when Rhyme and Reason set things right.
Another upsetting scene might be when Milo gest stuck in the Doldrums and encounters the Lethargians. They seem harmless, but it becomes obvious they're really pretty sinister during their song that ends up putting Milo to sleep. Then, when Tock comes along, he reveals that the Lethargians don't want anybody to do anything: even things like eating and breathing. Tock then helps get Milo out of the Doldrums. The Lethargians rise up in waves to try and stop them and just barely miss and end up cascading over a drop in a waterfall of yellowish goo.